It is easy to see that the strong Fréchet-Wilson property implies the Fréchet-Wilson property, which implies the weak Fréchet-Wilson property, which in turn implies Husdorffness of an \(M\) -distance space. Hausdorffness and the first two of the above properties were considered in the case \(M= \mathbb {R}\)  in [1]} as different ways to relax the triangle inequality. It is not hard to construct examples that show that generally speaking no two of the three properties are equivalent. Moreover, it is easy to see that the strong Fréchet-Wilson property is still weaker than the triangle inequality (in the sense that each \(EDM\) -metric space satisfies the strong Fréchet-Wilson condition), and as Example REF  from Section REF  shows, it is not equivalent to the Fréchet-Wilson property.
